CHAPTER 13 PHOTOMETRY AND SPECTROPHOTOMETRY
13.1 INTRODUCTION
This chapter describes a number of options useful in
photometry and spectrophotometry. Surface photometry is not
discussed here, but in Chapter 14. Several calculations
important in broadband photometry can be carried out with the
option MC. These include determinations of the average magnitude
over an instrumental and/or a standard band, the effective
wavelength over an instrumental and/or standard band, the
absolute flux, the K-correction over an instrumental and/or a
standard band, and the differential K-correction. Aperture
photometry is carried out with option BB. The construction of
photometry calibration curves is done with option BP. This
option will read the character file produced by BB and a standard
star file to produce the calibaration curve. Instrumental
magnitudes are then converted to standard magnitudes with this
same option. Note that the format of the standard star file
[MIIPS.PHOTOM]STANDARDS.DAT is scheduled for revision sometime in
1987. Photographic plates traced with a PDS microdensitometer
can be calibrated with option PD and converted to intensity with
option CA. As of this writing, option PD is not yet operational.
Several older routines, in use at Mt. Stromlo, are also
available. They are options OK, AF, PM, and ND, which enable
flux calibrations and spectrophotometry to be done on spectral
data. The data input to these four options must be in SAD files
of LAMBDA (wavelength) bintype. The user should therefore do all
flat-fielding, coincidence corrections and scrunching (into
wavelength bintype) before entry into this section. Sky
subtraction can also be done first, or the skies calibrated into
flux before subtraction. The option RE (REBIN) exists to convert
F(lambda) vs. lambda to F(nu) vs. frequency (and vv.). Option
AR (ARITHMETIC) can be used to produce magnitude vs. lambda or
frequency. The data-type (FITS keyword BUNIT: brightness unit)
and bintype (FITS keyword CTYPE1) are described in the SAD
header, and can be easily read by using the PH (PRINT HEADER)
command. The header information can also be edited with option
EH.
Examples of typical header info. follows:
KEY VALUE COMMENTS DESCRIPTIVE NOTES
(not on header)
CTYPE1= LAMBDA /metres : wavelength bintype
CRPIX1= 1.0 / : reference pixel
CRVAL1= 4020.0E-10 /metres : wavelength of pixel 1
CDELT1= 0.47E-10 /metres : increment per pixel
PIXOR= CENTRE / : flag specifying pixel
: origin (after 25-6-81)
BUNIT= FLAMBDA /erg/cm**2/sec/A : brightness
or BUNIT= FNU /erg/cm**2/sec/Hz : unit
Other information is generally created at time of observation.
You can insert any other info. for your own convenience using EH
Page 2
and option I (Insert). Other keywords recognised by options in
this section are:
RUN= 43 / : observational run no.
: not (yet) on PCA data
DWELL= 500.000 / : dwell time in secs
OBJECT= A VERY FAINT SOURCE / : ident. - user supplied
Values associated with these keywords appear in printed output at
various places and are a useful aid to bookeeping.
13.2 OPTION BP, PHOTOMCAL
13.2 OPTION BP, PHOTOMCAL
13.3 OPTION BB, BBEN
13.4 OPTION BP, PHOTOMTRY
13.5 OPTION PD, PDCAL
13.6 OPTION OK, OKECAL
A large compendium of flux standards (refs: Oke 1974, Stone
1977, Breger 1976 etc.) is stored in [MIIPS.DOC]OKESTD.FLX.
These standards are tabulated as ABv vs. wavelength (together
with bandpasses), where ABv = -2.5.LOG10[ F(nu) ] - 48.60. If a
required standard does not exist in the standard file, the user
must enter the values. Secondary standards (user specific) can
be created on your area by using PM with the SCANNER filter set.
This produces a file SECOND.FLX on your area - with an identifier
supplied by you. OK searches SECOND.FLX for a requested standard
if no match is found in the standard file.
An observed flux standard is photometered within the
tabulated bandpasses, and the observed magnitudes (OBSMAG)
differenced against the OKE magnitudes (AB). A plot of OBSMAG-AB
points vs. wavelength results, and the user can then delete
spurious points, and fit a smooth curve (poly or spline). The
final curve represents the instrumental correction (in
magnitudes) for each pixel, and is applied to the observational
data in AF (ABSFLX).
NOTES
a) Undue reliance should not be placed on a single flux
calibration standard. Observing at least 2 standards will enable
an objective assesment of instrumental photometric performance
and stability to be made. The error per flux point in some
standards can be quite high.
Page 3
b) Not all flux standards are calibrated throughout the optical
region - check this before observing. Only the defined region is
plotted in OKECAL - check the full calibration curve before
continuing.
c) Calibration curves can be averaged (AD or AR) and
intercompared by dividing (for example) or using LR (Linear
Regression). Option ME (MERGE) can be used to average
calibration curves over sub-regions of the observed wavelength
range.
FORMULAE and DEFINITIONS:
x : wavelength in A
v : frequency in Hz
Fx : F(lambda)
Fv : F(nu)
c : speed of light in A/sec
i) The default output from AF is F(lambda) vs lambda; the OKE
magnitudess are converted to:
OKEMAGx = -2.5 LOG10 Fx
= -2.5 LOG10 Fv - 2.5 LOG10 (c/x**2)
= ABv + 48.60 -2.5 LOG10 (c/x**2)
on entry and used in this form thereafter.
ii) The AIRMAS is calculated from the SAD header info (which must
therefore be correct !). In both OKECAL and ABSFLX the user can
4
select extinction coefficients (default slope of lambda4 term is
0.0092).
iii) The observed magnitudes are calculated as:
OBSMAGx = -2.5 LOG10 (RATE)
where RATE is the average rate (counts/sec/A) in the bandpass.
iv) The calibration curve is stored as:
K(I) = OBSMAGx - EXTCO*AIRMAS - OKEMAGx
= -2.5 LOG10 [obs. rate above atmos/F(lambda) ]
for each pixel, where:
LAMBDA(I) = start + (I-1)*increment.
The calibration curve has the FITS label: BUNIT = KLAMBDA.
These curves can be plotted in the normal way using PL, RP, WP,
QP etc.
13.7 OPTION AF, ABSFLX
Page 4
Option AF converts to absolute flux. Its output is either
F(lambda) vs. lambda or F(nu) vs. lambda. AF will also flip
the data-type for flux calibrated data from F(lambda) <--> F(nu):
the option will presume a flip is required for already calibrated
data, and ask you to verify this. This option takes the final
(averaged ?) calibration curve and applies it to the rest of the
data, which has otherwise been prepared (flat-fielding,
coincidence correction, scrunching etc) in exactly the same way
as the flux standard(s).
Select output as either:
1 F(lambda) vs. lambda
or 2 F(nu) vs. lambda
- although this can be flipped by a further application of AF.
NOTES
a) AIRMAS is calculated from header info - extinction coefs
should be as used in OKECAL.
b) For 1DPCA data applying a calibration curve appropriate to the
TOP array (say) to data in the BOTTOM array doesn't work.
Separate calibration curves must be made for each array. If no
standard is available, a secondary standard can be made from
existing data using PM (Photometry) with the SCANNER (50 A
rectangular bands) filter set.
c) For 2D data there are 2 observational possibilities: i) trail
the standard along the slit and produce a calibration curve
for each row - not yet implemented in SPECT, but can be. ii) Do
the objects at a fixed slit position, then sum constant
object rows and subtract constant sky rows to produce '1 row'
data. This is obviously unsatisfactory for extended objects. or
iii) use CD to produce a mask from the calib star and then use
this mask to extract (XT) individual line spectra to be
calibrated. The std may be masked, used in OK to -> calibration
and then EITHER the entire 2D map calibrated and the "line"
spectra extracted later OR the extraction may be done first.
(The opp is commutative.)
FORMULAE
for each pixel
i
OBSMAGx = -2.5 LOG10[ DATA(I)/(Dwellinc) ]
corrected mag
CORMAGx = OBSMAGx - EXTCO*AIRMAS
= -2.5 LOG10 [obs RATE above atmosphere]
OKEMAGx = CORMAGx - K(I) ( K from OKECAL )
= -2.5 LOG10[ Flambda ]
then output is
FLAMBDA = 10**[ -0.4*OKEMAGx ] erg/cm**2/sec/A
Page 5
or FNU = FLAMBDA * X**2/c erg/cm**2/sec/Hz
13.8 OPTION PM, PHOT2
This option accepts as input data-types FLAMBDA or FNU.
Various filter systems:
UBVRI (Buser 1978, Azusienis & Straizys 1969,
Bessell 1979)
DDO
CMT1T2 (Canterna 1979)
STROMGREN uvby (Crawford & Barnes 1970)
SCANNER 50 A rectangular bands
are compiled in [MIIPS.DOC]PHOTOM.SYS.
The filter transmissions are calibrated at varying
wavelengths appropriate to their bandwidths. The user selects a
filter system, and filters within the observational wavelength
region are interpolated (TSINC) onto the data grid. For each
filter, and each spectral row the following quantities are then
calculated:
filter mean Flambda
filter mean Fnu
effective wavelength
MAG -2.5 LOG10[ ] - 48.60 - ZERO
The zero points for each filter are included in the library, and
are adjusted to give good correspondence with the standard
system. To produce a secondary standard (stored in SECOND.FLX
on your area), use PM on one row of one map, select SCANNER
system, and give your standard a unique identifier when asked.
This standard can then be accessed by OKECAL in the normal way.
FORMULAE ( @ = Integral sign )
Fxdx = Fvdv
@ FxRxdx = @ FvRvdv : energy in filter
AVFLAM= = @ FxRxdx/@ Rxdx : filter mean Flambda
AVFNU = = @ FvRvdv/@ Rvdv
= @ FxRxdx/@ Rvdv/dx.dx : filter mean Fnu
EFFLAM= = @ FxRx.x.dx/@ FxRxdx : effective wavelength
MAG = -2.5 LOG10[ ] -48.60 - ZERO
13.9 OPTION ND, NDFILT
This subroutine selects a neutral density (or other) filter
from those available on disc file. filters are assumed to cover
the full wavelength range of the data individual filters are read
in at a wavelength spacing (del) given on the file and the
interpolated into the spacing (xinc) corresponding to the data.
the filter values are then returned in the array fnew which is in
pixel to pixel correspondence with the data.
name: name of the filter required
fold: filter values read from filter.set
xold: corresponding wavelength values
Page 6
fnew: array containing filter transmission values
at lambda=xst+(i-1)*xinc
xnew: corresponding wavelength values
xst: start wavelength corresponding to first pixel
xinc: inc. wavelength per pixel
ni: dimension of fnew (and of data)
file structure (t1,t2,...: %transmission values)
#filter name comments
start delta nvals
t(1) t(2) t(3) . . .
. . . . . .
. . t(nvals)
#filter name comments
start delta nvals
t(1) t(2) t(3) . . .
. . . .
References
Azusienis & Straizys 1969 Soviet Astron. A.J. 13, 316
Bessell 1979 PASP 91, 589
Breger 1976 Ap.J. Suppl. 32, 7
Buser 1978 AA 62, 411
Canterna 1979 Dud. Obs. Rep. 14, 489
Cousins
Crawford & Barnes 1970
Oke 1974 Ap.J. Suppl. 27, 21
Stone 1977